So now we're getting into Bayesian land.

And what it means is we really are Bayesian inference machines.

Now a key part to the Bayesian is this part of the formula.

And the key idea to Bayesian inference is you have two sources of information from which to make your inference.

And so, we're going to start by defining the basic semantics of a Bayesian network, and how it's constructed from a set of factors.

And to do that, I'm going to tell you about a framework which is very popular in statistics and machine learning of the last 50 years called Bayesian decision theory.

And the point about Bayesian decision theory is it gives you the mathematics of the optimal way to combine your prior knowledge with your sensory evidence to generate new beliefs.

As we go around, we learn about statistics of the world and lay that down, but we also learn about how noisy our own sensory apparatus is, and then combine those in a real Bayesian way.

So, we already have a little baby Bayesian network with three random variables, let's now take the other random variables and introduce them into the mix, so for example the SAT score of the student doesn't seem to depend on the difficulty of the course or on the grade the student gets in the course, the only thing it's likely to depend on, in the context of this model, is the intelligence of the student.